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Dispersion of the liquid crystal mixture E7 across the EM spectrum Chan-Shan Yang1 (楊承山), Ru-Pin Pan2, a (趙如蘋) and Ci-Ling Pan1, a (潘犀靈) 1 2 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 30013 Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan 30010 a [email protected], [email protected] The optical constants of liquid crystals (LCs) have been studied extensively in the past. The refractive indices of LCs are usually modeled by the extended Cauchy equation, which is a semi-empirical equation based on known optical constants of the material from the visible to the infrared. The corresponding birefringence (∆n) exhibit a general decreasing trend as the wavelength increased over this spectral range. For wavelengths much longer than the mean resonance wavelength (λ*~250 nm), i.e., infrared and beyond, ∆n is expected to approach a limiting but appreciable value. In this work, we have organized the refractive indices of E7, a liquid crystal mixture widely used for various applications, reported in the literature from the visible, near infrared, mid-infrared to the millimeter waves together with those of our data in the millimeter and sub-millimeter wave range measured by THz time-domain spectroscopy. This is shown in Fig. 1. The data from the visible to the mid-infrared can be fitted quite well by the Cauchy Equation reported by previous workers. The refractive indices in the THz (sub-millimeter wave), millimeter wave and microwave range, however, deviate significantly from the fitting curves. Similar trends can be seen from the available birefringence data across the entire spectrum and the fitting curves, as shown in Fig. 2. The above observations could be qualitatively explained. It is well-known that dispersion could vary significantly near resonances. Cyanobiphenyls, such as 5CB and 7CB, are major components of E7 and 5CB are known to have broad absorption features near 100, 140 and 165 cm-1, i.e., ~3 to 6 THz. In particular, there is a broad shoulder extending from the sub-THz frequencies to the absorption band near ~ 100 cm-1 assigned to the libration of the rigid molecule around its long axis. The far-infrared absorption spectrum of 7CB exhibits similar profiles with absorption bands near ~ 100, 160 and 180 cm-1. Thus we can qualitatively understand the deviation of the THz refractive indices of E7, because the known 3-parameter Cauchy Equation does not take into account these far-infrared resonances. 3.0 2.8 2.6 2.4 This work 2.2 Δn(fitting,Ref[1]) Δn(fitting,Ref[3]) Δn(fitting,Ref[2]) Δn(data,Ref[2]) Δn(data,Ref[2]) Δn(data,Ref[2]) Δn(data,Ref[4-6]) 0.44 0.40 0.36 0.32 n Δn 2.0 0.48 ne(fitting,Ref[1]) no(fitting,Ref[1]) ne(data,Ref[1]) no(data,Ref[1]) ne(fitting,Ref[3]) no(fitting,Ref[3]) ne(data,Ref[3]) no(data,Ref[3]) ne(data,Ref[4-6]) no(data,Ref[4-6]) 1.8 This work 0.28 0.24 0.20 1.6 0.16 1.4 0.12 1.2 1.0 0.08 -1 10 0 10 1 10 2 10 Wavelength (μm) Fig. 1 3 10 4 10 -1 10 0 10 1 10 2 10 Wavelength (μm) Fig. 2 3 10 4 10